Boyd (68 page)

Studies of human behavior reveal that the actions we undertake as individuals are closely related to survival, more importantly,
survival on our own terms. Naturally, such a notion implies that we should be able to act relatively free or independent of
any debilitating external influences
—otherwise that very survival might be in jeopardy. In viewing the instinct for survival in this manner we imply that a basic
aim or goal, as individuals, is to improve our capacity for independent action. The degree to which we cooperate, or compete,
with others is driven by the need to satisfy this basic goal. If we believe that it is not possible to satisfy it alone, without
help from others, history shows us that we will agree to constraints upon our independent action—in order to collectively
pool skills and talents in the form of nations, corporations, labor unions, mafias, etc.—so that obstacles standing in the
way of the basic goal can either be removed or overcome. On the other hand, if the group cannot or does not attempt to overcome
obstacles deemed important to many (or possibly any) of its individual members, the group must risk losing these alienated
members. Under these circumstances, the alienated members may dissolve their relationship and remain independent, form a group
of their own, or join another collective body in order to improve their capacity for independent action.

In a real world of limited resources and skills, individuals and groups form, dissolve and reform their cooperative or competitive
postures in a continuous struggle to remove or overcome physical and social environmental obstacles.
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In a cooperative sense, where skills and talents are pooled, the removal or overcoming of obstacles represents an improved
capacity for independent action for all concerned. In a competitive sense, where individuals and groups compete for scarce
resources and skills, an improved capacity for independent action achieved by some individuals or groups constrains that capacity
for other individuals or groups. Naturally, such a combination of real world scarcity and goal striving to overcome this scarcity
intensifies the struggle of individuals and groups to cope with both their physical and social environments.
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Against such a background, actions and decisions become critically important. Actions must be taken over and over again and
in many different ways. Decisions must be rendered to monitor and determine the precise nature of the actions needed that
will be compatible with the goal. To make these timely decisions implies that we must be able to form mental concepts of observed
reality, as we perceive it, and be able to change these concepts as reality itself appears to change. The concepts can then
be used as decision-models for improving our capacity for independent action. Such a demand for decisions that literally impact
our survival causes one to wonder: How do we generate or create the mental concepts to support this decision-making activity?

There are two ways in which we can develop and manipulate mental concepts to represent observed reality: We can start from
a comprehensive whole and break it down to its particulars or we can start with the particulars and build towards a comprehensive
whole.
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Saying it another way, but in a related sense, we can go from the general-to-specific or from the specific-to-general. A
little reflection here reveals that deduction is related to proceeding from the general-to-specific while induction is related
to proceeding from the specific-to-general. In following this line of thought can we think of other activities that are related
to these two opposing ideas? Is not analysis related to proceeding from the general-to-specific? Is not synthesis, the opposite
of analysis related to proceeding from the specific-to-general? Putting all this together: Can we not say that general-to-specific
is related to both deduction and analysis, while specific-to-general is related to induction and synthesis? Now, can we think
of some examples to fit with these two opposing ideas? We need not look far. The differential calculus proceeds from the general-to-specific—from
a function to its derivative. Hence is not the use or application of the differential Calculus related to deduction and analysis?
The integral calculus, on the other hand, proceeds in the opposite direction—from a derivative to a general function. Hence,
is not the use or application of the integral calculus related to induction and synthesis? Summing up, we can see that: general-to-specific
is related to deduction, analysis, and differentiation while specific-to-general is related to induction, synthesis, and integration.

Now keeping these two opposing idea chains in mind let us move on a somewhat different tack. Imagine, if you will, a domain
(a comprehensive whole) and its constituent elements or parts. Now, imagine another domain and its constituent parts. Once
again, imagine even another domain and its constituent parts. Repeating this idea over and over again we can imagine any number
of domains and the parts corresponding to each. Naturally, as we go through life we develop concepts of meaning (with included
constituents) to represent observed reality. Can we not liken these concepts and their related constituents to the domains
and constituents that we have formed in our imagination? Naturally, we can. Keeping this relationship in mind, suppose we
shatter the correspondence of each domain or concept with its constituent elements. In other words, we imagine the existence
of the parts but pretend that the domains or concepts they were previously associated with do not exist. Result: We have many
constituents, or particulars, swimming around in a sea of anarchy. We have uncertainty and disorder in place of meaning
and order. Further, we can see that such an unstructuring or destruction of many domains—to break the correspondence of each
with its respective constituents—is related to deduction, analysis, and differentiation. We call this kind of unstructuring
a destructive deduction.

Faced with such disorder or chaos, how can we reconstruct order and meaning? Going back to the idea chain of specific-to-general,
induction, synthesis, and integration the thought occurs that a new domain or concept can be formed if we can find some common
qualities, attributes, or operations among some or many of these constituents swimming in this sea of anarchy. Through such
connecting threads (that produce meaning) we synthesize constituents from, hence across, the domains we have just shattered.
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Linking particulars together in this manner we can form a new domain or concept—providing, of course, we do not inadvertently
use only those “bits and pieces” in the same arrangement that we associated with one of the domains purged from our imagination.
Clearly, such a synthesis would indicate we have generated something new and different from what previously existed. Going
back to our idea chain, it follows that creativity is related to induction, synthesis, and integration since we proceeded
from unstructured bits and pieces to a new general pattern or concept. We call such action a creative or constructive induction.
It is important to note that the crucial or key step that permits this creative induction is the separation of the particulars
from their previous domains by the destructive deduction. Without this unstructuring the creation of a new structure cannot
proceed—since the bits and pieces are still tied together as meaning within unchallenged domains or concepts.

Recalling that we use concepts or mental patterns to represent reality, it follows that the unstructuring and restructuring
just shown reveals a way of changing our perception of reality.
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Naturally, such a notion implies that the emerging pattern of ideas and interactions must be internally consistent and match-up
with reality.
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To check or verify internal consistency we try to see if we can trace our way back to the original constituents that were
used in the creative or constructive induction. If we cannot reverse directions, the ideas and interactions do not go together
in this way without contradiction. Hence, they are not internally consistent. However, this does not necessarily mean we reject
and throw away the entire structure. Instead, we should attempt to identify those ideas (particulars) and interactions that
seem to hold together in a coherent pattern of activity as distinguished from those ideas that do not seem to fit in. In performing
this task we check for reversibility as
well as check to see which ideas and interactions match-up with our observations of reality.
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Using those ideas and interactions that pass this test together with any new ideas (from new destructive deductions) or other
promising ideas that popped out of the original destructive deduction we again attempt to find some common qualities, attributes
or operations to re-create the concept—or create a new concept. Also, once again, we perform the check for reversibility and
match-up with reality. Over and over again this cycle of Destruction and Creation is repeated until we demonstrate internal
consistency and match-up with reality.
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When this orderly (and pleasant) state is reached the concept becomes a coherent pattern of ideas and interactions that can
be used to describe some aspect of observed reality. As a consequence, there is little, or no, further appeal to alternative
ideas and interactions in an effort to either expand, complete, or modify the concept.
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Instead, the effort is turned inward towards fine tuning the ideas and interactions in order to improve generality and produce
a more precise match of the conceptual pattern with reality.
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Toward this end, the concept—and its internal workings—is tested and compared against observed phenomena over and over again
in many different and subtle ways.
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Such a repeated and inward-oriented effort to explain increasingly more subtle aspects of reality suggests the disturbing
idea that perhaps, at some point, ambiguities, uncertainties, anomalies, or apparent inconsistencies may emerge to stifle
a more general and precise match-up of concept with observed reality.
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Why do we suspect this?

On one hand, we realize that facts, perceptions, ideas, impressions, interactions, etc. separated from previous observations
and thought patterns have been linked together to create a new conceptual pattern. On the other hand, we suspect that refined
observations now underway will eventually exhibit either more or a different kind of precision and subtlety than the previous
observations and thought patterns. Clearly, any anticipated difference, or differences, suggests we should expect a mismatch
between the new observations and the anticipated concept description of these observations. To assume otherwise would be tantamount
to admitting that previous constituents and interactions would produce the same synthesis as any newer constituents and interactions
that exhibit either more or a different kind of precision and subtlety. This would be like admitting one equals two. To avoid
such a discomforting position implies that we should anticipate a mismatch between phenomena observation and concept description
of that observation.
Such a notion is not new and is indicated by the discoveries of Kurt Gödel and Werner Heisenberg.

In 1931 Kurt Gödel created a stir in the World of Mathematics and Logic when he revealed that it was impossible to embrace
mathematics within a single system of logic.
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He accomplished this by proving, first, that any consistent system—that includes the arithmetic of whole numbers—is incomplete.
In other words, there are true statements or concepts within the system that cannot be deduced from the postulates that make-up
the system. Next, he proved even though such a system is consistent, its consistency cannot be demonstrated within the system.

Such a result does not imply that it is impossible to prove the consistency of a system. It only means that such a proof cannot
be accomplished inside the system. As a matter of fact since Gödel, Gerhard Gentzen and others have shown that a consistency
proof of arithmetic can be found by appealing to systems outside that arithmetic. Thus, Gödel’s Proof indirectly shows that
in order to determine the consistency of any new system we must construct or uncover another system beyond it.
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Over and over this cycle must be repeated to determine the consistency of more and more elaborate systems.
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Keeping this process in mind, let us see how Gödel’s results impact the effort to improve the match-up of concept with observed
reality. To do this we will consider two kinds of consistency: The consistency of the concept and the consistency of the match-up
between observed reality and concept description of reality. In this sense, if we assume—as a result of previous destructive
deduction and creative induction efforts—that we have a consistent concept and consistent match-up, we should see no differences
between observation and concept description. Yet, as we have seen, on one hand, we use observations to shape or formulate
a concept; while on the other hand, we use a concept to shape the nature of future inquiries or observations of reality. Back
and forth, over and over again, we use observations to sharpen a concept and a concept to sharpen observations. Under these
circumstances, a concept must be incomplete since we depend upon an ever-changing array of observations to shape or formulate
it. Likewise, our observations of reality must be incomplete since we depend upon a changing concept to shape or formulate
the nature of new inquiries and observations. Therefore, when we probe back and forth with more precision and subtlety, we
must admit that we can have differences between observation and concept description; hence, we cannot determine the consistency
of the system—
in terms of its concept, and match-up with observed reality—within itself.